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M23-10

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M23-10 [#permalink]

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New post 16 Sep 2014, 01:18
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There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question
[Reveal] Spoiler: OA

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Kudos [?]: 128915 [0], given: 12183

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Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128915 [0], given: 12183

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New post 16 Sep 2014, 01:18
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Official Solution:

There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question

The number of red roses must be a multiple of 21. It cannot be 42 or larger because this would mean that the number of white roses is 8 or larger and the total number of roses is 50 or larger. Because there are only 48 roses in the garden, the number of red roses is 21 and the number of white roses is 4. The number of black roses \(= 48 - 21 - 4 = 23\).

Answer: D
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M23-10 [#permalink]

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New post 30 Sep 2017, 23:42
This is a high quality question.

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M23-10 [#permalink]

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New post 01 Oct 2017, 00:42
Bunuel wrote:
There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question


let the red and white roses be \(21x\) & \(4x\)

Hence Black rose \(= 48-(21x+4x) = 48-25x\)

Now \(x=1\), because at \(x=2\), no of black roses will be negative which is not possible

Hence no of black rose \(= 48-25=23\)

Option \(D\)

Kudos [?]: 174 [0], given: 31

M23-10   [#permalink] 01 Oct 2017, 00:42
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